Question: x P(x)
0 0.25
1 0.05
2 0.15
3 0.55
The graph is a table in the top-left showing the probability distribution with x values 0, 1, 2, 3 and corresponding P(x) values 0.25, 0.05, 0.15, 0.55.
Find the mean of this probability distribution. Round your answer to one decimal place.
1. **State the problem:** We are given a probability distribution with values of $x$ and their corresponding probabilities $P(x)$.
2. **Formula for the mean (expected value) of a discrete probability distribution:**
$$\mu = \sum x_i P(x_i)$$
where $x_i$ are the values and $P(x_i)$ are their probabilities.
3. **Apply the formula:**
$$\mu = 0 \times 0.25 + 1 \times 0.05 + 2 \times 0.15 + 3 \times 0.55$$
4. **Calculate each term:**
$$0 \times 0.25 = 0$$
$$1 \times 0.05 = 0.05$$
$$2 \times 0.15 = 0.30$$
$$3 \times 0.55 = 1.65$$
5. **Sum the results:**
$$\mu = 0 + 0.05 + 0.30 + 1.65 = 2.00$$
6. **Round the answer:** The mean is $2.0$ when rounded to one decimal place.
**Final answer:**
$$\boxed{2.0}$$